From the control design perspective, however, the approach followed in the paper is more straightforward and insightful for deriving control-orientated Lagrangian dynamics compared to the approach of modeling the attitude using a Lagrangian function in conjunction with Lagrange multipliers [1]}, [2]}, [3]}, since it allows to explore the basic energy-conservation property and the additional properties of the Lagrangian dynamics, enabling to take full advantage of well developed control designs based on energy-shaping methodologies for a broad class of mechanical systems. To the best of the authors' knowledge, these properties are not revealed before in the literature attitude dynamics.
